Can anyone help with my Calc. II? Any type of advice would help. Question below...?

Given x=sin(t) - 1 , y=3 + cos(t) , 0%26lt;t%26lt;3(pi)/2 , eliminate the parameter to find an equation in terms of x and y.








Any kind of tips would help tremendously.. THank you!Can anyone help with my Calc. II? Any type of advice would help. Question below...?
Hello,





Given x=sin(t) - 1 , y=3 + cos(t) , 0%26lt;t%26lt;3(pi)/2 , eliminate the parameter to find an equation in terms of x and y.





Recall that x = r cost and y = rsint now let's solve both of these for r;


So cost = x/r and sint = y/r hence form our original equations we have:


x = y/r -1 and y = 3 + x/r now let's solve both for r:





Multiply both of tese equation by r giving us:


xr = y - r and yr = 3r + x now solve both of these for r and we have:





xr + r = y or r = y/(x+1) and yr - 3r = x or r = x/(y-3) now set these equal hence: y/(x+1) = x/(y-3) and cross multiply thus:





y(y-3) = x(x+1) or y^2 - 3y = x^2 +x





If you want them all on the right we obatin 0 = x^2 +x - y^2 + 3y








Hope This Helps!Can anyone help with my Calc. II? Any type of advice would help. Question below...?
Im not 100% on this but it might be helpful





y=3+cos[arcsin(x+1)]